Data processing method, data processing apparatus and processing apparatus

1. A data processing method for processing data for controlling a plasma processing apparatus, using a double exponential smoothing method, the method comprising the steps of:

obtaining, by a measuring device, data related to a plasma processing chamber in which a sample is subjected to a plasma process;

receiving, by a data input/output device, the obtained data;

storing the data in a storage;

calculating, by a calculation processing apparatus, using a double exponential smoothing method in which the data is set as input data, a first predicted value that is a predicted value of smoothed data and a second predicted value that is a predicted value of a gradient of the smoothed data, as output data;

calculating, by the calculation processing apparatus, using a double exponential smoothing method in which the second predicted value is set as input data, a third predicted value that is a predicted value of smoothed data and a fourth predicted value that is a predicted value of a gradient of the smoothed data, as output data;

detecting an end point of the plasma process based on the first predicted value, the second predicted value or the third predicted value, and the fourth predicted value; and

controlling the plasma processing apparatus based on the detected end point.

2. The data processing method according to claim 1 , further comprising the step of:

outputting, by the data input/output device, the first predicted value as a result of a data smoothing process, the second predicted value or the third predicted value as a result of a first differential process, and the fourth predicted value as a result of a second differential process, respectively.

3. The data processing method according to claim 1 , further comprising the steps of:

calculating, by the calculation processing apparatus, an approximate polynomial of an arbitrary number of pieces of data immediately following a start of data input; and

calculating, by the calculation processing apparatus, using the approximate polynomial, a fifth predicted value that is a predicted value of smoothed data preceding the start of data input, and a sixth predicted value that is a predicted value of a gradient of smoothed data preceding the start of data input,

wherein, in the step of calculating, using the double exponential smoothing method, the first predicted value that is the predicted value of smoothed data and the second predicted value that is the predicted value of the gradient of the smoothed data, the first predicted value and the second predicted value are calculated as the fifth predicted value and the sixth predicted value are set as initial values.

4. A data processing method for processing data for controlling a plasma processing apparatus, using a double exponential smoothing method, the method comprising the steps of:

obtaining, by a measuring device, data related to a plasma processing chamber in which a sample is subjected to a plasma process;

receiving, by a data input/output device, the obtained data;

storing the data in a storage;

calculating, by a calculation processing apparatus, an approximate polynomial of an arbitrary number of pieces of data following a start of data input;

calculating, by the calculation processing apparatus, using the approximate polynomial, a first predicted value that is a predicted value of smoothed data preceding a start of data input, and a second predicted value that is a predicted value of a gradient of smoothed data preceding a start of data input;

subjecting the data to a double exponential smoothing process as the first predicted value and the second predicted value are set as initial values;

detecting an end point of the plasma process based on a result of the double exponential smoothing process; and

controlling the plasma processing apparatus based on the detected end point.

5. The data processing method according to claim 4 , wherein smoothing parameters are varied in accordance with an error between input data and smoothed data, wherein the data is processed while making a lower limit value of a variable range of the smoothing parameters greater than zero.

6. The data processing method according to claim 4 , wherein when N denotes a natural number of 3 or more, the data is subjected to an N-tuple exponential smoothing process, and the N-tuple exponential smoothing process is a data process to successively perform a data smoothing process on the data and perform a first to (N−1)th smoothing processes to gradient of smoothed data.

7. The data processing method according to claim 6 , wherein

when the N is 3, a 3-tuple exponential smoothing process calculates a predicted value of the smoothed data, a predicted value of gradient of the smoothed data and a predicted value of gradient in gradient of the smoothed data.

8. A plasma processing method for subjecting a sample to a plasma process, the method comprising the steps of:

measuring light emission data in the plasma process of the sample;

processing, using a responsive double exponential smoothing method and smoothing parameters are varied in accordance with an error between the measured light emission data and a predicted value of smoothed light emission data, the light emission data while making a lower limit value of a variable range of the smoothing parameters greater than zero; and

controlling the plasma process of the sample according to a detected plasma processing state of the sample or a change in the detected plasma processing state of the sample on the basis of at least one of a result of a data smoothing process calculated by the responsive double exponential smoothing method, a result of a first differential process calculated by the responsive double exponential smoothing method, and a result of a second differential process calculated by the responsive double exponential smoothing method.